Apparatus and method 3d artificial hyperbolic reef for affecting surface waves

ABSTRACT

A 3D artificial hyperbolic reef system for producing plunging or barreling waves for surfing in a body of water propagates waves over a 3d hyperbolic reef which forms a wave breaking surface which has a slope sufficient to cause the waves to break in a plunging and barreling way as the waves traverse the 3d hyperbolic reef. The waves are artificial generated by a wave generating machine or device with a slope sufficient to break in a plunging and barreling way. Multiple waves are generated in a set frequency from the wave generator along the wave generator house (berm) side of the 3d artificial hyperbolic reef to produce a wave that peels laterally along the reef to produce a wave suitable for tube riding. 
     Aspects of the invention provide a wave surf pool including at least one 3D hyperbolic artificial reef. The 3D artificial reef can include an inclined slope traversing the reef from the tip of the 3D hyperbolic reef to the open end, or the back side of the 3D hyperbolic reef.

CITATIONS

-   Richard Mladick and Richard Carnahan, US2009/0151064 A1, Filed Dec.     17, 2008 -   Fred Cobylyn, WIPO Patent Application WO/2009/132378 -   Garrett T. Johnson, US2008/0060123 A1, Filed Aug. 8, 2007 -   Gary Ross, U.S. Pat. No. 5,207,531, Filed Sep. 3, 1991, Issued May     4, 1993 -   Albert Cohen, U.S. Pat. No. 5,342,145, Filed Apr. 1, 1993, Issued     Aug. 30, 1994 -   Mauricio Carvalho de Andrade, U.S. Pat. No. 7,052,205, Filed Jan.     29, 2002, Issued May 30, 2006 -   Richard Carnahan, U.S. Pat. No. 7,497,643, Filed Oct. 18, 2006,     Issued Mar. 3, 2009 -   Dan Whittenburg, U.S. Pat. No. 6,715,958, Filed Jul. 29, 2002,     Issued Apr. 6, 2004 -   Richard Carnahan, U.S. 2003/0077122 A1, Filed, Dec. 2, 2002 -   Richard Carnahan, U.S. 2001/0014256 A1, Filed, Mar. 26, 2001 -   Kenneth Hill, U.S. Pat. No. 6,019,547, Filed Oct. 6, 1997, Issued     Feb. 1, 2000 -   Kenneth Hill, U.S. Pat. No. 6,336,771, Filed Jan. 3, 2000, Issued     Jan. 8, 2002 -   Howard Foote, U.S. Pat. No. 6,102,616, Filed Apr. 9, 1999, Issued     Aug. 15, 2000 -   Garrett T. Johnson, U.S. 2010/0088814 A1, Filed Oct. 13, 2009

FIELD OF INVENTION

The present invention relates generally to apparatus and or fixed or detachable 3D artificial hyperbolic triangle reefs for affecting surface waves which propagate along the surface of a body of water.

Although the present invention will be described with particular reference to affecting surface waves which propagate specifically along the surface of a pool, surf pool, lake, pond, and river.

The present invention relates generally to surfing pools in which waves suitable for surfing are generated artificial by wave generating machines or devices. This invention particularly relates to surfing pools, in which the waves that are generated are suitable for tube riding by surfing, boogie boarding, body boarding, and kayaking.

BACKGROUND OF THE INVENTION

Surfing pools for generating waves suitable for surfing have been previously proposed and in some instances are used commercial in surfing pools or surfing parks. Previous surfing pools known to the present inventor have not been capable of generating waves over a 3D artificial hyperbolic reef structure, suitable for tube riding. Tube riding is riding a boogie board, surf board inside a breaking wave. The surfer typically rides the shoulder or the base of the wave at the leading edge of the break as it progresses laterally along the wave front, and the surfer can also ride inside the breaking part of the wave. In contrast to plunging or barreling waves are spilling waves, which break without forming tubes or barrels. For the purpose of our invention we will be focusing on plunging breaking waves that are formed by a 3D artificial hyperbolic reef.

Current reefs that have been tried to be patented are two dimensional or single dimensional artificial reefs. The current invention is a three dimensional artificial hyperbolic reef structure that are intentional designed and shaped with different slopes and contours to maximize wave height shape and form.

A number of geometers made attempts to prove the parallel postulate by assuming its negation and trying to derive a contradiction, including Proclus, Ibn al-Haytham (Alhacen), Omar Khayyám, Nasir al-Din al-Tusi, Witelo, Gersonides, Alfonso, and later Giovanni Gerolamo Saccheri, John Wallis, Johann Heinrich Lambert, and Legendre.[2] Their attempts failed, but their efforts gave birth to hyperbolic geometry.

The theorems of Alhacen, Khayyam and al-Tusi on quadrilaterals, including the Ibn al-Haytham-Lambert quadrilateral and Khayyam-Saccheri quadrilateral, were the first theorems on hyperbolic geometry. Their works on hyperbolic geometry had a considerable influence on its development among later European geometers, including Witelo, Gersonides, Alfonso, John Wallis and Saccheri. In the 18th century, Johann Heinrich Lambert introduced the hyperbolic functions and computed the area of a hyperbolic triangle.

In the nineteenth century, hyperbolic geometry was extensively explored by János Bolyai and Nikolai Ivanovich Lobachevsky, after whom it sometimes is named. Lobachevsky published in 1830, while Bolyai independently discovered it and published in 1832. Carl Friedrich Gauss also studied hyperbolic geometry, describing in a 1824 letter to Taurinus that he had constructed it, but did not publish his work. In 1868, Eugenio Beltrami provided models of it, and used this to prove that hyperbolic geometry was consistent if Euclidean geometry was. The term “hyperbolic geometry” was introduced by Felix Klein in 1871.

There are four models commonly used for hyperbolic geometry: the Klein model, the Poincaré disc model, the Poincaré half-plane model, and the Lorentz model, or hyperboloid model. These models define a real hyperbolic space which satisfies the axioms of a hyperbolic geometry. Despite their names, the first three mentioned above were introduced as models of hyperbolic space by Beltrami, not by Poincaré or Klein.

-   1. The Klein model, also known as the projective disc model and     Beltrami-Klein model, uses the interior of a circle for the     hyperbolic plane, and chords of the circle as lines. This model has     the advantage of simplicity, but the disadvantage that angles in the     hyperbolic plane are distorted.

The distance in this model is the cross-ratio, which was introduced by Arthur Cayley in projective geometry.

-   2. The Poincaré disc model, also known as the conformal disc model,     also employs the interior of a circle, but lines are represented by     arcs of circles that are orthogonal to the boundary circle, plus     diameters of the boundary circle. -   3. The Poincaré half-plane model takes one-half of the Euclidean     plane, as determined by a Euclidean line B, to be the hyperbolic     plane (B itself is not included). Hyperbolic lines are then either     half-circles orthogonal to B or rays perpendicular to B. Both     Poincaré models preserve hyperbolic angles, and are thereby     conformal. All isometries within these models are therefore Möbius     transformations. The half-plane model is identical (at the limit) to     the Poincaré disc model at the edge of the disc -   4. The Lorentz model or hyperboloid model employs a 2-dimensional     hyperboloid of revolution (of two sheets, but using one) embedded in     3-dimensional Minkowski space. This model is generally credited to     Poincaré, but Reynolds (see below) says that Wilhelm Killing and     Karl Weierstrass used this model from 1872. This model has direct     application to special relativity, as Minkowski 3-space is a model     for spacetime, suppressing one spatial dimension. One can take the     hyperboloid to represent the events that various moving observers,     radiating outward in a spatial plane from a single point, will reach     in a fixed proper time. The hyperbolic distance between two points     on the hyperboloid can then be identified with the relative rapidity     between the two corresponding observers.

The four models essentially describe the same structure. The difference between them is that they represent different coordinate charts laid down on the same metric space, namely the hyperbolic space. The characteristic feature of the hyperbolic space itself is that it has a constant negative scalar curvature, which is indifferent to the coordinate chart used. The geodesics are similarly invariant: that is, geodesics map to geodesics under coordinate transformation. Hyperbolic geometry generally is introduced in terms of the geodesics and their intersections on the hyperbolic space.[5]

Once we choose a coordinate chart (one of the “models”), we can always embed it in a Euclidean space of same dimension, but the embedding is clearly not isometric (since the scalar curvature of Euclidean space is 0). The hyperbolic space can be represented by infinitely many different charts; but the embeddings in Euclidean space due to these four specific charts show some interesting characteristics.

Since the four models describe the same metric space, each can be transformed into the other. See, for example, the Beltrami-Klein model's relation to the hyperboloid model, the Beltrami-Klein model's relation to the Poincaré disk model, and the Poincaré disk model's relation to the hyperboloid model.

SUMMARY

It is the primary objective of the present invention to provide a detachable or fixed 3D artificial hyperbolic reef to affect the surface waves in a pool, lake, pond and river, which produces plunging and barrel type breaking waves that exhibit progressive breaking laterally along the wave front so the waves can be used for tube riding. Another object of this invention is to provide a surfing pool which produces plunging type wave substantially at a constant wave peeling rate and frequency along the wave front to facilitate reading of the waves by the surfers as they break over the 3D hyperbolic artificial reef. Other objects and advantages will become apparent from the following detailed description and the accompanied drawings.

In accordance with the present invention, the foregoing objectives are realized by forming a 3D hyperbolic reef having a wave breaking surface which inclines upwardly towards the shore of the surf pool at a pre determined angle, and generating and forming waves on the wave generator house side of the reef. Propagating toward the shore the waves having steepness sufficient to cause the waves to break in a plunging barreling way as the wave traverse the wave breaking surface of the 3D hyperbolic reef.

To produce waves that break in a plunging way, the slope of the inclined portion of the 3D reef surface is preferably 1/25 and is most preferably at a range of 1/6 or 1/10, 1/15. When the slope is less then 1/25 the wave breaks without plunging. The acute angle or (peel angle) between the wave front and the wave breaking surface on the 3D reef surface is preferably in the range of 30 degrees to 70 degrees. We have found that the optimal peel angle is around 45 degrees. At angles less than 30 degrees the wave tends to peel to fast, making it very difficult for the surfer to keep up with the peel speed of the wave. If the peel angle is greater than 70 degrees excessive energy can be lost on wave breaking, and the wave can become undesirable small. By selecting different peel angels it is possible to change the range of difficulty of the wave sin the surf pool. For a more difficult surfing pool the peel angels should be closer to 30 degrees and for ales difficult wave the peel angel should be set at closer to 70 degrees.

The 3D hyperbolic reef will be submerged in water at the bottom of the surf pool such that the waves are able to propagate over the 3D artificial hyperbolic reef. The positioning of the hyperbolic reef in the surf pool will be determined many factors such as pool design, types of waves, wave heights, water depth, etc. Strategic placing of the solid reefs in the surf pool will maximize the propagating of the waves of the reef surface. The artificial hyperbolic 3D reef will affect the height of the wave, shape of the wave and the rate at which they peel and break. The solid reef is able to cause a wave which propagates over the reef after it passes over the reef.

The solid reef design allows for surfers riding the wave over to reef to fall into deeper water upon falling and not make contact with the 3D reef structure.

The upper part (top) of the 3D hyperbolic triangle reef surface will contain a series of circle structures that are evenly spaced apart on top of the solid reef surface. We have found that the circle structures perform the best. The structures can be made out of any circle structure such as a PVC pipe, bamboo, etc. These structures can be shaped in a rectangle, triangle or square structures as well. It has been found that these circle structures affect the waves shape and form by inhibiting the base of each wave by spreading or widening as it propagates over the solid reef. This function increases the wave height of each wave and the overall shape and form of each wave for surfing. The circular structures on the surface of the solid reef should stretch from one end of the reef to the other. Going from an upper end and running to a lower end of the reef. For optimal performance the circular structures should be equal spaced apart and run parallel to each other along the reef surface. It is preferred that each circular structure have an identical shape and size.

The 3D reef will be either fixed or detachable and can be placed anywhere with in the surf pool. The solid reef hyperbolic structure will be anchored to the bottom of the surf pool by cement anchoring stations or other securing methods and strategically placed in the surf pool. The Hyperbolic reefs can also be shaped and made to natural contour the bottom of the surf pool, pond, lake, river or lagoon.

BRIEF DESCRIPTION OF THE DRAWINGS

In order that the invention may be more fully understood and put into practice, a preferred embodiment thereof now will be described with reference to the accompanied drawings.

DETAILED DESCRIPTION OF THE DRAWINGS

Before any aspect of the invention are explained in detail, it should be understood that the invention is not limited to its application in the details of construction and the arrangement of components set forth in the following description or shown in the following drawings. The invention is capable of other aspects and of being practiced or of being carried out in various ways. Also, it should be understood that the phraseology and terminology used herein is for the purpose of description and should and should not be regarded as limited.

Description of FIG. 1:

This figure shows the “Premier” or first placed hyperbolic reef twists and shapes and contours to the natural slope of the surf pool, lake, pond, and river or lagoon bottom. The front of the hyperbolic reef is slightly elongated to slow the breaking of the wave down for surfers to have a more controlled take off point. The cross section view of the premier reef shows the twisting contouring feature of the hyperbolic shaped reef.

Description of FIG. 2:

FIG. 2 shows the hyperbolic reefs placed in the surf pool and are strategically placed in the pool in a hyperbolic fashion to maximize the wave breaking points and to maximize wave height and form. The hyperbolic shaped reefs are placed in succession to create multiple wave breaking points in the surf pool.

Description of FIG. 3:

This figures shows the “Triennial Hyperbolic Reef” or the third or last reef to be placed in the surf pool. This figure shows the Triennial Hyperbolic Reef is shaped in a hyperbolic fashion to allow the wave to break in shorter distances or beach break on the beach side of the surf pool.

Description of FIG. 4:

This figure shows the “The second” hyperbolic reef strategically shaped in a hyperbolic fashion and form as to make the sides (the legs) of the hyperbolic reef longer then the premiere reef in the pool. The longer hyperbolic sides of the reef create longer surf rides in the pool and sustains the wave breaking form as the wave transverses the reef. The figure shows the cross section view of the second hyperbolic reef in its hyperbolic twisting shaping form.

Description of FIG. 5:

This figure shows the Hyperbolic Reef with baffles or circular structures placed along the top of the hyperbolic reef. The baffles placed along the top of the artificial hyperbolic reef slows the wave down, increase wave height and keeps the form of the wave as it transverses over the hyperbolic reef. 

1-30. (canceled)
 31. A 3D artificial Hyperbolic triangle shaped reef for affecting surface waves propagating along a surface of a body of water, the reef comprising an inclined upper surface that could include a plurality of circular structures, the reef being submergible in the body of water such that the waves are able to propagate over the hyperbolic reef, and such that the upper surface faces towards the waves as the waves propagate towards the reef. The 3D artificial hyperbolic reef can be shaped in many different forms and shapes. The preferred shape of the hyperbolic reef is a triangle hyperbolic triangle shape. The hyperbolic reef can also be in 2D (two dimensional form).
 32. The 3D artificial Hyperbolic Triangle shaped reef of claim 31, further comprising a 3 dimensional hyperbolic artificial reef. The 3D artificial hyperbolic reef will be shaped in a hyperbolic triangle manner. In hyperbolic geometry, a hyperbolic triangle is a figure in the hyperbolic plane, analogous to a triangle in Euclidean geometry, consisting of three sides and three angles. The relations among the angles and sides are analogous to those of spherical trigonometry; they are most conveniently stated if the lengths are measured in terms of a special unit of length analogous to a radian. In terms of the Gaussian curvature (K) of the plane this unit is given by. In all the trig formulas stated below the sides a, b, and c must be measured in this unit. In a hyperbolic triangle the sum of the angles A, B, C (respectively opposite to the side with the corresponding letter) is strictly less than a straight angle. The difference is often called the defect of the triangle. The area of a hyperbolic triangle is equal to its defect multiplied by the square of R: A characteristic property of hyperbolic geometry is that the angles of a triangle add to less than a straight angle. In the limit as the vertices go to infinity, there are even ideal hyperbolic triangles in which all three angles are Distances in the hyperbolic plane can be measured in terms of a unit of length, analogous to the radius of the sphere in spherical geometry. Using this unit of length a theorem in hyperbolic geometry can be stated which is analogous to the Pythagorean theorem. If a, b are the legs and c is the hypotenuse of a right triangle all measured in this unit then: The cosh function is a hyperbolic function which is an analog of the standard cosine function. All six of the standard trigonometric functions have hyperbolic analogs. In trigonometric relations involving the sides and angles of a hyperbolic triangle the hyperbolic functions are applied to the sides and the standard trigonometric functions are applied to the angles. For example the law of sines for hyperbolic triangles is: Unlike Euclidean triangles whose angles always add up to 180° or π radians the sum of the angles of a hyperbolic triangle is always strictly less than 180°. The difference is sometimes referred to as the defect. The area of a hyperbolic triangle is given by its defect multiplied by R² where. As a consequence all hyperbolic triangles have an area which is less than R²π. The area of an ideal hyperbolic triangle is equal to this maximum. As in spherical geometry the only similar triangles are congruent triangles.
 33. The 3D artificial Hyperbolic reef of claim 31, further comprising: The 3D hyperbolic triangle artificial reef causes the wave to split down the middle and causes the wave to break into two separate waves a left barreling wave and a right barreling wave.
 34. The 3D Artificial hyperbolic triangle reef of claim 31, further comprising: The circular structures are fixed to the top of the reef; however the circular structures can also have a detachable feature.
 35. The 3D Artificial Hyperbolic triangle Reef of claim 31, further comprising: The 3D artificial reef functions in a hyperbolic fashion as the wave leaves the wave generator apparatus and as the wave transverses over the hyperbolic shaped reef the wave will travel along the hyperbolic reef until it finds its breaking point.
 36. The 3D Artificial Hyperbolic Triangle reef of claim 31, further comprising: The 3D hyperbolic reef becomes hyperbolic, (hyperbolic function) because it shapes and twists to the increasing contour of the surf pool, lake, lagoon, or pond bottom. The twisting shaping of the hyperbolic shaped reef is what causes the breaking of the wave in different breaking forms and in different water depths.
 37. The 3D Artificial Hyperbolic Triangle Reef of claim 31, further comprising: The 3D hyperbolic artificial reef of claim 1, wherein the upper surface includes an upper end, and a lower end, and wherein the circular structures extend from the upper end to the lower end, parallel to each other.
 38. The 3D Artificial Hyperbolic Triangle Reef of claim 31, further comprising: The hyperbolic artificial reef of any one of the preceding claims, wherein the circular structures are spaced apart from each other.
 39. The 3D Artificial Hyperbolic Triangle Reef of claim 31, further comprising: The 3D artificial hyperbolic reef wherein the circular structures are hollow.
 40. The 3D Artificial Hyperbolic Triangle Reef of claim 31, further comprising: The 3D hyperbolic artificial reef of any one of the preceding claims, wherein each of the circular structures has a profile selected from the group comprising: a straight linear profile; a T- shaped profile; a profile including a circular portion and a straight linear portion extending from the circular portion; a triangular profile; a circular profile; and a rectangular or square profile.
 41. The 3D Artificial Hyperbolic Triangle Reef of claim 31, further comprising: The 3D hyperbolic artificial reef wherein each of the circular structures includes a pipe or tube, made from PVC or Bamboo or other similar shaped and hollow structures or material.
 42. The 3D Artificial Hyperbolic Triangle Reef of claim 31, further comprising: The 3D hyperbolic artificial reef can be anchored to the surf pool bottom by cement anchor stations or by other securing methods. The 3D Hyperbolic reef can also be made to contour natural to the bottom of the surf pool, lake, pond, river or lagoon.
 43. The 3D Artificial Hyperbolic Triangle Reef of claim 31, further comprising: The 3D hyperbolic artificial reef increases and sustains the height of the wave as it travels over the upper surface of the reef.
 44. The 3D Artificial Hyperbolic Triangle Reef of claim 31, further comprising: The 3D artificial hyperbolic reef improves the plunging and barreling shape of the wave as it passes over the upper surface of the reef.
 45. The 3D Artificial Hyperbolic Triangle Reef of claim 31, further comprising: The 3D artificial hyperbolic reef maintains the shape and form of the wave as it passes over the surface of the reef.
 46. The 3D Artificial Hyperbolic Triangle Reef of claim 31, further comprising: The 3D hyperbolic artificial reef has different slopes that transverse back from the front of the solid reef that affect the shape, size and form of the wave as the wave passes over the reef surface.
 47. The 3D Artificial Hyperbolic Triangle Reef of claim 31, further comprising: The 3D hyperbolic artificial reef has different slopes that transverse down the back side of the reef into deeper water that affect the shape size and form of the wave as it passes over the reef surface.
 48. The 3D Artificial Hyperbolic Triangle Reef of claim 31, further comprising: There are different shaped and designed 3D hyperbolic artificial reefs that are placed strategically within the surf pool. Lagoon, lake or pond or river, that create different waves at different points in the surf pool. By placing these reefs at different points and depths and locations within the surf pool create different waves for different levels of surfers.
 49. The 3D Artificial Hyperbolic Triangle Reef of claim 31, further comprising: The surf pool contains multiple 3D artificial hyperbolic triangle reefs or other shaped hyperbolic reefs that are strategically placed in the surf pool to maximize the number of surfers that can surf in the surf pool at one time.
 50. The 3D Artificial Hyperbolic Triangle Reef of claim 31, further comprising: The elongated front part of the 3D artificial hyperbolic reef causes the wave to break slightly or gradually allowing surfers to easily catch and drop in on the wave before the wave accelerates. 